Question

Задача №1 Из колоды карт в 36 листов наудачу вынимают по одной карте, не возвращая их в колоду. Какова вероятность того, что при первом извлечении появится туз, а при втором - не туз. Задача№2 В Коробке 10 красных карандашей и 5 зелёных. Наугад извлекают два карандаша. Какова вероятность того, что оба карандаша красные _____________________ Решить задачи путём комбинаторики

Answer 1

Problem 1: Probability of drawing an Ace on the first draw and a non-Ace on the second draw

To solve this problem, we need to calculate the probability of drawing an Ace on the first draw and a non-Ace on the second draw from a deck of 36 cards, without replacement.

The deck contains 4 Aces and 32 non-Aces. Let's calculate the probability step by step:

1. Probability of drawing an Ace on the first draw: - Number of Aces in the deck: 4 - Total number of cards in the deck: 36 - Probability of drawing an Ace on the first draw = 4/36 = 1/9

2. Probability of drawing a non-Ace on the second draw: - Number of non-Aces in the deck after the first draw: 32 - Total number of cards remaining in the deck after the first draw: 35 - Probability of drawing a non-Ace on the second draw = 32/35

To find the probability of both events occurring, we multiply the probabilities of each event:

Probability = (1/9) * (32/35) = 32/315

Therefore, the probability of drawing an Ace on the first draw and a non-Ace on the second draw is 32/315.

Problem 2: Probability of drawing two red pencils

To solve this problem, we need to calculate the probability of drawing two red pencils from a box containing 10 red pencils and 5 green pencils, without replacement.

Let's calculate the probability step by step:

1. Probability of drawing a red pencil on the first draw: - Number of red pencils in the box: 10 - Total number of pencils in the box: 15 - Probability of drawing a red pencil on the first draw = 10/15 = 2/3

2. Probability of drawing a red pencil on the second draw, given that the first draw was a red pencil: - Number of red pencils remaining in the box after the first draw: 9 - Total number of pencils remaining in the box after the first draw: 14 - Probability of drawing a red pencil on the second draw = 9/14

To find the probability of both events occurring, we multiply the probabilities of each event:

Probability = (2/3) * (9/14) = 3/7

Therefore, the probability of drawing two red pencils is 3/7.

Please let me know if you need any further assistance!